The thermodiffusion analysis of thin polymer films

Thermochmucu Act4 190 (1991) 65-76 Elsevler !Zcrence Publishers B V , Amsterdam

The thermodiffusion

65

analysis of thin polymer films

V.V. Teplyakov A V Topchlev Institute of Petrochemrcal Synthesis, The USSR Academy of Sciences, Moscow (USSR) (Received 29 January 1991)

Abstract Although the solubmty and diffusivity of gases and vapours through polymers are temperature-dependent properttes shown by all such systems, the Qffusion of several gases through a polymer and the diffusion of the same gas through different polymers have not been mvestigated systematically. We have found that the diffusivlty (D), solubthty (S), permeabmty (P) parameters and their temperature dependence for gases m polymers can be used to descnbe the permeabihty parameters of other gases and vapours m the polymer materials in questron. Noble gases were used as probes to determme the temperature-dependent diffusion and the diagnostics of the permeabmty features of various gases, 1 e bi- and multi-atomic simple gases, lower hydrocarbons and some acid gases, through polymer thm films INTRODUCTION

In recent years thin polymer films of specified diffusion properties have gained importance in several fields of science and technology, e.g. in electronics (for coatings), in chemical and nuclear technology (for the separation of gas mixtures) and in agriculture (for the storage of ahmentary products under preserving conditions). As it is very complicated and time consuming to obtain quantitative information on the permeability of various gases through thin polymer films, we attempted to gain the maximum amount of information about these properties of thin films at different temperatures by making the mimmum amount of gas &ffusion measurements. This was possible by using inert gases to characterize the thin-film diffusion properties. The thermodiffusion analysis based on these measurements was used to predict the permeability through solid polymer films of other gases and vapours of inorganic and organic origm. Inert gases have been used to study the permeability properties of solids for many years [l-9]. The results of numerous studies on the inert-gas

Presented at the Forum of Thermoanalysts, Prague, 1990. 0040-6031/91/$03.50

0 1991 - Elsevrer Science Pubhshers B.V All rights reserved

66

release from solids, and the methods of inert gas introduction into solids, etc., have been reviewed by Balek [lo]. It has been shown that the thermodiffusion method can be used as a quality-control tool in the manufacture of thin polymer films of specified properties, e.g. gas-permeable membranes, coatings of specific permeability as required by the electronics industry, isolating and preserving coatings, and capsules that give controlled release of the active components of drugs. Despite considerable theoretical and experimental research into gas transport through various classes of polymers, exlstmg theoretical approaches cannot satisfactorily explain all the observed facts. This is especially true for copolymers and composite polymeric materials, the components of which may be present in different physical and phase conditions. In addition, the current state of knowledge does not allow the formulation of detailed criteria of chemical structure, physical and phase states and other physicochemical properties that are required to guide the screening or synthesis of homo- and co-polymers for preparing potential coatings and other thin films having controlled selective gas transport. In the present paper an attempt is made to analyse and describe the known correlations of the permeability parameters of polymers in order to show the possibility of selecting the chemical properties that are most important in controlling the selective permeability of gas transport and of predicting the gas permeability and its temperature dependence of thin polymeric films. THE MAIN PERMEABILITY

PARAMETERS

OF THIN POLYMERIC

FILMS

Experimental techniques and mathematical methods are available for the analysis of simple and moderately complex diffusion phenomena in polymers. The methods of analysing experimental data on diffusion have been reported in the literature (see, for example, refs. 11-21). Modem techniques permit the main gas-transfer parameters (i.e. the coefficients of diffusivity D, solubility S and permeability P) to be determmed reliably for single gases and vapours in polymers. In the simplest case P = DS = Qh/AAp

(1)

where Q is the steady-state flux of gas under the pressure difference Ap through an area A of membrane thickness h. The experimental difficulties connected with the determination of diffusion parameters are not covered here because they have been widely discussed in the literature (see, for example, refs. 11-13, 16-18, 22-24). It is necessary, however, to bear in mind the possibility that gas-permeability parameters depend on concentration, space and time. In particular, they may depend on the extent of cross-linking in the polymer [11,12], the extent

67

of crystallinity in partly crystalline polymers [25], the annealing temperature and plasticization of glassy polymers [11,12], and the morphology and organization in copolymers and blends of polymers [26-291. With mixtures of permeants, one penetrant may influence the permeability of another [30] and, especially in glassy polymers under high gas pressures, a fraction of the permeant may be immobilized [16,22,30]. Account must also be taken of the consequences of experimental errors connected with, for example, the variation in the thickness of film samples and the use of approximate methods for treating experimental data [19-21,311. As permeation through thin polymeric films mcludes both sorption and desorption, particular caution must be taken when deriving diffusion data solely from kinetic sorption experiments [ll-13,22,23]. Bearing in mind that the migration of molecules through solids by diffusion is by molecular thermojumping, if the structure of the polymer does not change over some temperature interval the temperature dependences of the permeability parameters are approximated by exponential functions P = POexp( -E,/RT)

(2)

D = Da exp( -E,/RT)

(3)

S = S,, exp( - AHJRT)

(4)

where ED is the activation energy of gas diffusion and AH, is the heat of gas solution. The balance of the above temperature dependences for a given polymer characterizes its temperature coefficient of permeability. In this paper the permeability parameters (derived mainly from permeability experiments) for rare gases, a number of permanent gases and hydrocarbons (C, to C,) and a number of polymeric materials are considered. The temperature dependences of these characteristics are also used in the analysis. The polymers for which data were taken into consideration include polydienes, polysiloxanes, polyolefins, halogen and silicon containing carbon chain polymers, polymeric esters and ketones, polyamides and polyaromatic compounds. In addition, random and block copolymers of polydienes, polydimethyl siloxane (PDMS), polyvinyltrimethylsilane (PVTMS) and polyolefins were included. The data were taken from refs. [25,26,28,31-431. Equation (1) shows that the permeability coefficient P reflects the kinetic (D) and thermodynamic (S) aspects of gas transfer. The permeability coefficients of, for example, argon vary over eight orders of magnitude in different polymers, while D varies over nine orders and S over 1.5 orders. The ratios of the permeabilities of the different gases vary widely over a range of polymers. For example, for the pair He/Kr the permeability ratio varies from less than 1 in PDMS, NR and PE [32] to more than lo5 in PAN [34]. (Abbreviations of polymer names are listed in Table 1.)

68 TABLE 1 The correlation coefficients (eqns. (5) and (8)) for estimatmg the gas permeabdity of polymerrc films [36,37,41,43] No

parameters

Coefficient (X 10’)

Polymer

KI

K2

K3

-785 -694 -815 -842 - 8.71 -783 -722 -796 - 8.16 -740 -743 - 7.56 -729 -773 - 7.15 -749 -709

0.100 0 185 0 211 0.225 0.250 0 324 0 347 0.373 0 427 0451 0.269 0.108 0 471 0.556 0.578 0 603 0.947

- 4.70 -407 -547 -574 - 5.95 -556 -484 - 4.42 - 5.87 -541 -5 16 -500 -538 -552 - 5.59 - 5.60 -565

077 0 85 0.85 0.92 0 79 0.80 0.93 0.94

92.ga 80:20 50 : 50 80.20 73 : 27 68 : 32 61.39

-824 -8.00 - 8.16 -804 - 8.05 - 7.96 - 7.97

0.184 0.253 0 199 0 248 0.282 0.316 0.357

-540 - 5.63 -533 -560 - 5.66 - 5.74 - 5.78

072 0 85 0.74 1.06

polystyrene (ABA) 73.27 59.41 Polyarylate : polydrmethylsrloxane (AB), 46:54 Polyvmyltnmethylskne poly&methylsloxane (AB) 80:20 64 : 36 60.40

- 8.47 -8.43

0.142 0 171

- 5.50 - 5.64

110 116

-8.19

0.121

-482

075

-762 - 7.84 - 7.83

0 282 0.219 0.188

-453 - 4.51 - 4.86

0.76 0 88 0 80

Homopolymers

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15

Polydrmethylsrloxane (PDMS) Polytnmethylsdylpropyne (PMSP) Polybutadrene (PB) Polyethylene (PE) (p = 0 914 g cm-3) Polyethylene (PE) (p = 0 968 g cmM3) Polymethylvmylether (PMVE) Polyvmyltrnnethylsdane (PVTMS) Polyphenylenoxtde (PPO) Polyarmde-11 (PA-11) Polyvmylacetate (PVA) 298 K 350 K 400K Polyethylmethacrylate (PEMA) Polyethylenterephtalate (PETPH) Polyvmylacetate (Z’s) (PVA) Polymethylvmylketone (PMVK) Polyacrylomtnle (PAN)

Random copolymers 16 Butadrene styrene

17 18 19 20 21 22

Ethylene propylene Butadtene acrylomtrrle

Block copolymers 23 Polybutadrene

24 25 26 27 28

102 0 77 0.51 0 37 0.98 0.98

101 0.74 1.47

109 114 117

a Parts weight for weight.

Such wide variability m the permeability and selectivity towards gases of organic polymers whuzh, as a class, have rather similar densities and elemental compositions, has led to considerable research into the mechanism of gas diffusion and into the influence of the physical and chemical properties of the polymer on its gas-permeation parameters.

69

THE CORRELATION OF PERMEABILITY PARAMETERS

Several correlations of the coefficients of diffusivity (D), solubility (S) and permeability (P) of gases and vapours to their properties and those of polymers have already been reported [ll-16,22-241. Correlations between permeabilities, and polymer properties (such as density and extent of crystalhnity in polyolefins [25], glass transition temperatures and melting points of glassy polymers [12,44], and the cohesive energy density of polyaromatic compounds [45]) have been proposed. Correlations of P with gas properties such as molecular size and critical temperature have been suggested [44, 46,471. Whilst such correlations are valid only for particular groups of homopolymers and often suffer from errors even in the order of magnitude of the predicted values, they do point the way to a more general approach to the understanding of the gas permeabilities of polymeric materials and membranes. If the permeabilities of, for example, the rare gases m a series of polymers are considered to depend on any one property of the polymers (such as their densities) or of the gases (for example their atomic weights) it can be seen from Fig. 1 that the permeabilities of the “heavy” gases in polymers such as PDMS, NR, PE and PMSP are htgh by comparison with those of the “light” ones i.e. P&P,, > 1 [32,48]. However, the opposite is true for polymers such as PAN, PMVK, PVA and PVTMS [33-361. These correlations of the permeabilities are characterized by different functional graphs which cross one another. For this reason it must be recognized that to base the correlations of P values on any property of the polymer or gas will not be adequate. There are two possible approaches to relating permeability data to polymer chemical structure: the Permachor and the solubility space factor concepts. The Permachor correlation makes use of a scheme of additive (positive or negative) contributions from the chemical structural elements of the polymer to its permeability [12,13]. However, unlike classical additive properties, these structural contributions are not the same for all gases or for all polymers. The Permachor concept can only be applied to known experimental data of homopolymers. It is not a reliable predictive tool for copolymers, for new polymers or for polymenc blends, composites, and so on. The solubility space factor method was suggested in an attempt to establish a more general basis for permeability prediction. It allows for the effect of the thermal expansion of the polymeric film. The thermal-expansion coefficient can be estimated by means of a method of additive contributions [13,49]. While this method shows some promise, it has the same disadvantages as the Permachor concept. The diffusion coefficient (D) of penetrants in a polymer usually decreases with increasing dimensions of the penetrant molecule. The critical volume,

70

-12

NR PVTMS

-14

PE

-16

PVA

-16

PMVK

P B

r

t.

-20

PAN

t

0

1

2 log M

Fig. 1. Dependence of the gas permeabtity (as log P) on the atormc we@ts of the mert gases (as log M) at 298 K. PMSP, poly(l-(tnmethylsdyl)-1-propyne), PDMS, polydnnethylsfioxane, NR, polylsopene, PVTMS, polyvmyltnmethyls&me; PE, polyethylene, PVA, polyvmylacetate, PMVK, polymetbylvmylketone; PAN, polyacrylomtnle The UNtS of P are mol m s-l m- * Pa-’ (see eqn (1))

der Waals volume, collision diameter, cross-section or any combination of these may be selected as a measure of the molecular dimension [25,32,36,38,42,50-521. A number of authors have noted the difficulties of analysing diffusion data using such properties, and several scales of molecular diameters obtained by different calculation methods have been explored [48,53-601. An analysis of the correlation between D and the molecular diameter has been carried out for more than 50 polymeric materials [36,37]. It was found that the dependence of D on molecular diameter for the rare gases and a number of multi-atomic gases was optimally expressed by Van

log 0, = Kr - K, . d,2

(5) where 0, is in m2 s-r and d, (in nm) is the effective molecular diameter. These diameters were obtained by comparing the diffusion coefficients of the vanous gases in different polymers with those of the rare gases [36,43]. The values K, and K, are dependent on temperature (Table 1).

71

Equation (5) is valid for homopolymers and copolymers under different phases and physical conditions, and both coefficients in eqn. (5) are isothermally constant for any polymer. Equation (5) is used on the hypothesis that durmg diffusion jumps bi- and multi-atomic molecules are oriented in the direction of the maximum molecular dimension of the molecule [25,36,42]. In support of this hypothesis it may be noted that the effective cross-sections of multi-atomic gases obtained by comparison with the rate gases are lower than the gas-phase equilibrium values [43]. In all cases increasing the effective cross-section of the permeant leads to a lowering of D. The diffusion coefficients of different gases in polymers increase with temperature in accordance with the Arrhenius equation (eqn. (3)). The activation energy increases virtually in proportion to the effective cross-section of the permeant [26,55]; this holds for both the rare gases and multiatomic gases. When K, and K, are known for a polymer, the coefficients of diffusivity and the Arrhenius activation energies in that polymer can be estimated for about 12 gases and a number of hydrocarbons up to C,. A large number of K, and K, values have been published already [36,37]. It should be noted that values of K, and K2 obtamed by using data for only two or three rare gases under different temperatures can be used to estimate the permeability of polymeric films to a number of gases at the desired temperature (for some data on different polymeric materials see Table 1). The values of K, and K, for a new polymer can be obtamed by collecting diffusion data on two or three rare gases. Although the correlation equation (eqn. (5)) can be used satisfactorily to predict the values of D for many gases and vapours in different polymers (including polymers of unknown composition) on the basis of only minimum experimental data, a simple empirical approach is insufficient for estimating the values of K, and K,. These coefficients are determined not only by the chemical structure of the polymer but also by physical properties such as density, extent of crystallinity, glass temperature, interchain interactions, macrochain packing and supra-molecular organization. For complex polymeric materials, i.e. structured copolymers blends and composites, Kl and K, also depend on the phase structure organization. Although it must be expected that under isothermic conditions Kl and K, depend on many polymer properties, it should also be noted that there are predominating trends. Thus Kl varies relatively little from one polymer to another, while K2 increases continuously with the increasing cohesive energy density (CED) of the polymers. For example: in PDMS (CED = 238 MJ mV3), K, = +O.l; and in PAN (CED = 1033 MJ me3 [49]) K, = +0.947. This is shown particularly clearly by the values for the homopolymers listed in Table 1. For copolymers, an increase in the mole fraction of the monomer residue possessing the higher CED leads to an increase in K,

72

(see, for example, the butadiene : acrylonitrile copolymers in Table 1). It should be noted that the maximum values of K, are for glassy polymers with polar side groups attached to the main chain. Medium values of K2 are found for glassy polymers with non-polar side groups and the smallest values of K2 are found for rubber-like polymers. While the kinetic factor (D) in the permeabihty coefficient decreases with increasing cross-section of the migrating molecule, the thermodynamic factor (S) normally increases. More correctly, the solubilities (S) of gases and vapours in different polymers [ll-13,22,25,36-381, by analogy with solubilities in liquids, increase in accordance with T,, Tb or the force constant of the (6-12) mtermolecular potential. Such correlations can be derived theoretically by equating the chemical potentials of the permeant in the gas and in the solid polymenc phase [23] log S = O.Oll( a/k) + constant The temperature Clausius-Clapeyron

(6)

coefficient of the solubility can be expressed using the equation

log S = log S,, - AH,/2.303

RT

(7)

where AH, is the molar heat of solution. Equations (6) and (7) suggest that the index of the exponent (0.011) is independent of the nature of the polymer and that the solubility depends only on the Lennard-Jones potential e/k. There is no established view on which property to choose as the characteristic one of a polymer. It is known from experimental data that the greater the free volume fraction of the polymer the greater are the solubilities of gases in it [15,46]. On generalizing this approach, the correlation equation log S,=K,+K&/k)

(8)

is proposed [36,37,43]. The coefficients K3 and K4 obtained from such correlation plots are dependent on temperature and are listed in Table 1. The values of K, and K4 for any polymer can be estimated by determining the solubilities of two or three simple gases, e.g. rare gases. The effective values of q/k which determine the solubilities of other gases in polymers can be obtained from the correlation plots if the solubility of the gases m a single polymer is known [43]. Regarding the values of K3 and K., under isothernnc conditions (Table l), K4 varies relatively little between different polymers and is quite close to the theoretical value of 0.011. It can be seen, however, that K4 increases slowly with increasing polarity of the polymer. Although the values of K, are not constant the variations are not large and show no clear trend with the chemical composition of the polymer.

73

Finally, the sorption heats (AH,) are found [55] to depend linearly on the values of e/k, as is consistent with eqn. (7), i.e. the estimation of these values for a number of gases can be based on minimum experimental data obtained for inert gases.By combining the correlation equations (eqns. (5) and (8)) a general relationship can be obtained for the permeability coefficients of polymeric films log P, = log 0, + log S, = Kl + K, - K,d,2 + K4q/k

(9)

It should be noted that, in rubber-like polymers, including partly crystalline ones and one glassy polymer (PMSP), the solubility of the gases and vapours is the predominant factor and in these cases the permeability of the more soluble gas is greater than that of the less soluble one. However, the reverse is true for glassy polymers. An example of this can be seen in Fig. 1 where, in the rubbery polymer PDMS, P,, IS less than Px,, whereas in the

Fig 2. The gas permeability changes for polyvmylacetate (PVA) at the operatmg temperatures of (a) 250 K, (b) 300 K, (c) 350 K, (d) 400 K. Axes effective cross se&on of the dlffusant molecule (x), the {6-12}-potentml force constant of the &ffusant molecule (y), and the permeabhty coefflclents for PVA flhn (z)

74

glassy polymer PVTMS, P,, is greater than P,,. Other situations are possible and, for example, the selective gas permeability of copolymers CXIl take intermediate values between those of the homopolymers [28]. An example of thermodiffusion analysis for thin films obtained by using data for inert gases is shown in Fig. 2. In this case the reliefs of gas permeability of PVA vary from the unpermeable condition (the exceptions are for He and H,) at 250 K up to the very permeable condition (in relation to acid gases and hydrocarbons) at 350-400 K. It should be noted that once the coefficients Ki to K4 of a polymer have been established, an estimate can be made of the permeability of any gas for which the effective diameter and force constant are known. Thus the potential of any polymer film to allow the permeation of particular gases can be assessed without carrying out additional experimental work. Since the values of Kl to K4 can be determined from a small number of permeability measurements made with inert gases without any knowledge of the chemical composition of the polymer, it is possible to assess the value of commercially available polymeric films and coatings, m terms of their isolating or permeable properties, under operating temperatures other than those for which they were originally produced. CONCLUSION

The thermodiffusion method can be used to assess the gas-permeability parameters of polymer thin films. The values of the inert gas diffusivity (D), solubility (S), permeability (P) and the thermocharacteristics ED, AH, and Ep measured in the required temperature region allow the D, S, P, ED, AH, and Ep values of various other gases and vapours in the polymer film m question to be predicted, even when the chemical composition of the polymer is not available. The results obtained using the thermodiffusion method can be used in the manufacture and control of thin polymer films having specified properties, such as gas-permeable membranes, coatings of controlled permeability (as required in electronics), isolating and preserving coatings, and controlled-release drug capsules. REFERENCES 1 2 3 4 5 6 7 8

C Jech, Int. J. Appl. Rad Isotopes, 8 (1965) 179. HJ. Mat&e, Phys. Stat. Sol., 18 (1966) 285 R Kelly, C. Jech and H.J. Matzke, Phys. Stat Sol, 25 (1968) 641 R Kelly and C. Jech, Proc Br. Ceram. Sot., 9 (1967) 243. K.B Zaborenko and I.N. Beckman, Radlokhumya, 10 (1968) 268. K.B. Zaborenko and I.N. Beckman, Radokhinuya, 10 (1968) 382. V. Balek, J Mater Scl., 4 (1969) 919. V Balek, Z Anorg. Aug. Chem., 380 (1971) 82

75 9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

42 43 44 45 46

V BaIek, J Radioanal Chem, 30 (1976) 599 V BaIek, Thermoc~. Acta, 22 (1977) 1. J Crank and G.S Park, Diffusion m Polymers, Academic Press, New York, 1968, p 445 S.A Reythnger, Permeability of Polymeric Mater&. Khmnya, Moscow, 1974, p. 268. S T. Hwang and K Kammermeyer, Membranes m Separations, Wiley-Intersctence, New York, 1975, Chap 3. N I Ntkolaev, Diffusion m Membranes, Khumya, Moscow, 1980, p 232. D.R Lloyd (Ed.), Materials Science of Synthetic Membranes, ASC Symposmm Series No 269, American ChemtcaI Society, Washmgton DC, 1985, p. 492. P M Bungay, H.K. LonsdaIe and M.N. de Pmho (Eds.), Synthetic Membranes: Sctence, Engmeermg and Apphcatrons, NATO AS1 Series C, Vol. 181, D. Reidel, Dordrecht, 1986, p. 733 J. Crank, The Mathematics of Diffusion, 2nd ed , Clarendon Press, Oxford, 1975. W Jost, Dtffunon m Sohds, Liqutds, Gases, Academtc Press, New York, 1960 I N Beckman, Radlokhimiya (USSR), 23 (1981) 267; 23 (1981) 425; 25 (1983) 252. G Pahnai and K. Olah, J. Membrane Sci , 21 (1984) 161 A A Shvyryaev and I.N. Beckman, Vestmk MGU, Chem., 22 (1981) 517. P. Meares (Ed.), Membrane Separation Processes, Elsevler, Amsterdam, 1976, p. 600 V Stannett, J. Membr. Sa., 3 (1978) 97. J Comyns, Polymer Permeabmty, Elsevler, Amsterdam, 1985. A S Mchaels and H.J. BixIer, J. Polymer Sci., 50 (1961) 393, 413. H. Odany, K Taua, N. Nemoto and M. Kuraba, Bull. Inst. Chem Res , 53 (1975) 216 JA. Barrie and K Munday, J. Membr. Su., 13 (1983) 175. A.L Ievlev, V V. Teplyakov, S.G. Durgaryan and N S. Nametkm, Dokl USSR Acad. Sci , 264 (1982) 1421. J.H Petropoulos, J. Polymer Scr : Polymer Phys. Edn , 23 (1985) 1309 T E Whyte (Ed ), Industrial Gas Separations, ASC Symposmm Series, American Chemical Society, Washington DC, 1983. H. Yasuda and K. Rosengren, J Appl Polymer Sci , 8 (1970) 467. J E Lundstrom and R.J. Bearman, J. Polym Scl: Polym. Phys. Edn ,12 (1974) 97. S.M. Allen, V Stamiett and H.B. Hopfenberg, Polymer, 22 (1981) 912. S M Allen, M. FUJLI,V Stannett, H P. Hopfenberg and J L. Wilhams, J. Membr. Set , 2 (1977) 153 J. Brandrup and E.H Immergut (Eds.), Polymer Handbook, 2nd edn., Whey-Interscience, New York, 1975, p 111-229. V.V Teplyakov and S G. Durgaryan, Vysokomol. Soedm, Ser. A, 26 (1984) 1498, 26 (1984) 2159, 28 (1986) 564 V.V Teplyakov, A.L Ievlev and S.G Durgaryan, Vysokomol. Soedin., Ser. A, 27 (1985) 818 V.V. VoIkov, N.S. Nametkm, E.G Novrtsky and S.G Durgaryan, Vysokomol. Soedm, Ser. A, 21 (1979) 920, 927. S.G Durgaryan, E.G. Novltsky, Y P. Yampolsky and N.S Name&m, Z PrtkIadn. Chrm , 52 (1979) 1132. J H Flynn, Polymer, 23 (1982) 1325. T Nakagawa, Membranes 111Gas Separation and Enrichment: Proceedings of the Fourth BOC Priestly Conference, Special Pubhcation No 62, Royal Society of Cherrnstry, London, 1986, p. 351 A.R. Berens and H.B Hopfenberg, J Membr Sci , 10 (1982) 283 V.V. Teplyakov and P. Meares, GAS Sep. Purim , 4 (1990) 65 C C. Li, AIChE J , 20 (1974) 1015 G H Hammon, K Ernst and JC Newton, J Appl Polymer Sci , 21 (1977) 1989 A Peterhn, J Macromol. Sci, B 11 (1975) 57.

76 47 T W. Sarge, Indust. Eng Chem., 19 (1947) 396. 48 R.C. Reid, J.M. Prausmtz and T.K Sherwood, The Properties of Gases and Liquids, 3rd edn., McGraw-Hi& New York, 1977. 49 D.W. Van Krevelen, Properties of Polymers, EIsevler, Amsterdam, 1976. 50 G S. Park, Trans. Faraday Sot., 47 (1951) 1007. 51 P J. Kokes and F A. Long, J. Am Chem. Sot., 75 (1953) 6142. 52 N S. Tikhomuova, Y M. Mahnsky and V.L. Karpov, Vysokomol. Soedm., 2 (1961) 211. 53 H.A. Stuart, MolekuIstruktur (Molecular Structure), Spnnger-Verlag, Berhn, 1967, p. 84. 54 J.A. Dean, Lange’s Handbook of Chemrstry, McGraw-Hi& New York, 1979, Part 3, p 3. 55 J.O. I-hrshfelder, R B. Brrd and E L. Spotz, J. Chem. Phys., 16 (1948) 968 56 A HeydweIIer, Arm. Phys ,42 (1913) 1273. 57 G.A Cook, Argon, Hehum and Rare Gases, Vol. 1, Interscience, New York, 1961, p. 13. 58 V N. Kondratyev, Struktura atomov 1 molekul (The Structure of Atoms and Molecules), Physmetgis, Moscow, 1959, p. 469 59 J.O. Hirshfelder, Ch.F. Curtiss and R.B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1954, p 1100. 60 C.L. De Ligm and N.G. Van der Veen, Chem. Eng. Scl., 27 (1972) 391.